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This invention relates to measurement of pressure using quartz pressure transducers and more particularly to a system and method for both statically and dynamically calibrating transducer output signals for affects of temperature and temperature transients.
Piezoelectric quartz crystal oscillators are often used as pressure or temperature sensors. These devices are generally designed so that pressure or temperature induced stresses cause the resonant frequency of the device to change. The resonant frequency can be measured or recorded and converted to pressure or temperature values. These devices are quite accurate and have become standard devices for measuring pressure in boreholes, for example oil and gas wells, where very high pressures may be encountered and need to be accurately measured.
The quartz crystal oscillators are actually sensitive to both pressure and temperature. The crystal orientation may be selected to, for example, increase the sensitivity to pressure while decreasing sensitivity to temperature and vice versa. However, a crystal designed for pressure sensing is still sensitive to temperature. That is, at a fixed pressure, the crystal resonant frequency still changes with temperature. Likewise, a crystal designed for temperature sensing will change resonant frequency in response to changing pressure at a constant temperature.
The relationship of resonant frequency of a quartz crystal oscillator to, for example, pressure is nonlinear. That is, the actual or gauge pressure cannot be obtained by multiplying the frequency by a constant. High order polynomial functions have been developed for converting the frequency of a pressure transducer, the pressure frequency, to actual pressure. These polynomials may be developed based on actual measurement of pressure frequencies at a plurality of known stabilized pressures and temperatures. Once the polynomial has been developed for a given transducer, it may be used in field operations to provide pressure outputs from pressure frequencies or it may be used to process pressure frequency data which has been recorded previously. So long as the pressure frequency measurements are taken when the quartz crystal temperature has stabilized and an accurate temperature reading is available, the resulting pressure measurements are very accurate and accepted as an industry standard.
The conversion of pressure or temperature frequencies to actual pressure and temperature values is referred to a calibration of the sensor outputs. It not only converts the frequencies to normal pressure and temperature values, like pounds per square inch and degrees, but compensates for nonlinearities and the affect of temperature on pressure frequency and vice versa. However, such calibration assumes that the transducer conditions have stabilized when readings are taken. The polynomial is developed based on frequencies measured only after the temperature of the transducers has equalized throughout the entire quartz crystal.
It is known that temperature transients cause errors in calibration of quartz sensor outputs with the known calibration functions. For example, if the temperature of fluid surrounding a quartz transducer is changed, the pressure frequency will change indicating a change in pressure, even if the ambient fluid pressure actually remains constant. After a period of time in which the temperature throughout the quartz crystal equalizes to the new temperature, the pressure frequency will return to the value expected for the actual ambient pressure and temperature. The temperature transient causes thermal gradients in the crystal which creates a real pressure stress on the quartz crystal until the temperature of the crystal equalizes. For example, if ambient temperature drops, the outer surface of the crystal cools first and shrinks. This applies a compressive force (in addition to the force applied by ambient fluids) on the inner portion of the crystal which is still at a higher temperature. When the crystal temperature equalizes, the temperature induced stress is eliminated.
Measurement errors caused by transients complicate and increase the cost of measuring pressures and temperatures in wellbores. Temperatures and pressures are measured in wells in various types of operations. In a logging operation, a sonde having various transducers, including pressure and temperature transducers, may be continuously moved up or down in a borehole to produce a continuous record of pressure, temperature, etc. which may be plotted versus depth position. If the device passes from a first region at a first temperature to a second region at a second temperature, the pressure frequency will change even if no actual change in pressure occurred. By moving the sonde slowly, the errors can be minimized, but the increased time translates to increased cost of the operation. In other operations, such as drill stem tests, a device may measure temperature and pressure at a fixed location in a well while fluids are produced from, or injected into, the well. Such operations cause pressure changes which need to be measured accurately, but also cause temperature transients which cause errors in the pressure measurements.
It would be desirable to provide a calibration system and method for quartz oscillator transducers which not only calibrate the transducer outputs for static conditions, but also dynamically correct for transient conditions.
In the present invention, one or more temperature difference values, i.e. change of temperature with time, are used to correct temperature transient errors in pressure frequency outputs of a quartz pressure transducer. In a preferred form, multiple temperature difference values are coupled through a tapped delay line to a transfer function which corrects the temperature transient errors.
In one embodiment of the invention, a single transfer function or model is used to calibrate pressure frequencies from a quartz pressure transducer. Inputs to the model include the pressure frequency, a temperature sensor output, and a time spaced series of temperature difference values. The single model provides both static and dynamic calibration of the pressure frequency outputs of the quartz pressure transducer.
In another embodiment, separate static and dynamic calibration functions are used. A static calibration function receives pressure frequency values and temperature sensor outputs and produces a statically corrected pressure value. A dynamic calibration model receives at least one temperature difference value and generates an output indicating the error in pressure frequency caused by temperature transients. The error value may be combined with the statically calibrated value to provide a pressure value corrected for both static conditions and temperature transient conditions.